derivative a^{2x+3}

解答

导数

a^{2 x + 3}

2 a^{2 x + 3} ln (a)

求解步骤

\frac{d}{d x} (a^{2 x + 3})

使用指数法则:

a^{b} = e^{b l n (a)}

a^{2 x + 3} = e^{(2 x + 3) l n (a)}

= \frac{d}{d x} (e^{(2 x + 3) l n (a)})

使用连锁律:

e^{(2 x + 3) l n (a)} \frac{d}{d x} ((2 x + 3) ln (a))

= e^{(2 x + 3) l n (a)} \frac{d}{d x} ((2 x + 3) ln (a))

\frac{d}{d x} ((2 x + 3) ln (a)) = 2 ln (a)

= e^{(2 x + 3) l n (a)} \cdot 2 ln (a)

e^{(2 x + 3) l n (a)} = a^{2 x + 3}

= 2 a^{2 x + 3} ln (a)

d er i v a t i v e \frac{4}{( 9 + x ^{2} )}

d er i v a t i v e (x + 1)^{3} (5 - x)

d er i v a t i v e y = (x^{2} + 1) \cdot (x + 1)

d er i v a t i v e \frac{( 2 + x )}{( 2 - x )}

d er i v a t i v e arctan (x^{2} + 1)